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A329216 Decimal expansion of 2^(5/12).

%I A329216 #18 Apr 28 2024 16:27:02
%S A329216 1,3,3,4,8,3,9,8,5,4,1,7,0,0,3,4,3,6,4,8,3,0,8,3,1,8,8,1,1,8,4,4,5,2,
%T A329216 7,7,4,9,1,2,3,9,0,2,1,2,6,2,5,1,9,8,2,9,6,9,3,8,9,7,0,8,1,2,1,5,7,2,
%U A329216 2,0,6,6,7,8,4,1,1,3,9,2,0,2,3,7,1,4,8,1,5,9,1
%N A329216 Decimal expansion of 2^(5/12).
%C A329216 2^(5/12) is the ratio of the frequencies of the pitches in a perfect fourth (e.g., D4-G4) in 12-tone equal temperament.
%H A329216 Wikipedia, <a href="https://en.wikipedia.org/wiki/Equal_temperament#Comparison_with_Just_Intonation">Equal temperament</a>
%H A329216 Wikipedia, <a href="https://en.wikipedia.org/wiki/Twelfth_root_of_two">Twelfth root of two</a>
%H A329216 <a href="/index/Mu#music">Index entries for sequences based on music</a>
%F A329216 Equals 2/A328229.
%t A329216 First[RealDigits[2^(5/12), 10, 100]] (* _Paolo Xausa_, Apr 28 2024 *)
%o A329216 (PARI) default(realprecision, 100); 2^(5/12)
%Y A329216 Frequency ratios of musical intervals:
%Y A329216 Perfect unison:   2^(0/12) = 1.0000000000
%Y A329216 Minor second:     2^(1/12) = 1.0594630943...  (A010774)
%Y A329216 Major second:     2^(2/12) = 1.1224620483...  (A010768)
%Y A329216 Minor third:      2^(3/12) = 1.1892071150...  (A010767)
%Y A329216 Major third:      2^(4/12) = 1.2599210498...  (A002580)
%Y A329216 Perfect fourth:   2^(5/12) = 1.3348398541...  (this sequence)
%Y A329216 Aug. fourth/
%Y A329216 Dim. fifth:       2^(6/12) = 1.4142135623...  (A002193)
%Y A329216 Perfect fifth:    2^(7/12) = 1.4983070768...  (A328229)
%Y A329216 Minor sixth:      2^(8/12) = 1.5874010519...  (A005480)
%Y A329216 Major sixth:      2^(9/12) = 1.6817928305...  (A011006)
%Y A329216 Minor seventh:   2^(10/12) = 1.7817974362...  (A329219)
%Y A329216 Major seventh:   2^(11/12) = 1.8877486253...  (A329220)
%Y A329216 Perfect octave:  2^(12/12) = 2.0000000000
%K A329216 nonn,easy,cons
%O A329216 1,2
%A A329216 _Jianing Song_, Nov 08 2019